On the solutions of the equation 𝑥^{𝑚}+𝑦^{𝑚}-𝑧^{𝑚}=1 in a finite field

Ke, Wen Fong; Kiechle, Hubert

doi:10.1090/S0002-9939-1995-1234628-4

On the solutions of the equation $x^ m+y^ m-z^ m=1$ in a finite field
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Proc. Amer. Math. Soc. 123 (1995), 1331-1339 Request permission

Abstract:

An explicit formula for the number of solutions of the equation in the title is given when a certain condition, depending only on m and the characteristic of the field, holds.

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